An Alternative Robust Estimator of Average Treatment Effect in Causal Inference

Abstract

Summary The problem of estimating the average treatment effects is important when evaluating the effectiveness of medical treatments or social intervention policies. Most of the existing methods for estimating the average treatment effect rely on some parametric assumptions about the propensity score model or the outcome regression model one way or the other. In reality, both models are prone to misspecification, which can have undue influence on the estimated average treatment effect. We propose an alternative robust approach to estimating the average treatment effect based on observational data in the challenging situation when neither a plausible parametric outcome model nor a reliable parametric propensity score model is available. Our estimator can be considered as a robust extension of the popular class of propensity score weighted estimators. This approach has the advantage of being robust, flexible, data adaptive and it can handle many covariates simultaneously. Adopting a dimension reduction approach, we estimate the propensity score weights semiparametrically by using a nonparametric link function to relate the treatment assignment indicator to a low-dimensional structure of the covariates which are formed typically by several linear combinations of the covariates. We develop a class of consistent estimators for the average treatment effect and study their theoretical properties. We demonstrate the robust performance of the estimators on simulated data and a real data example of investigating the effect of maternal smoking on babies’ birth weight.

Sufficient Dimension Reduction for Feasible and Robust Estimation of Average Causal Effect

“…We now apply the methods presented to estimate the average causal effect of maternal smoking during pregnancy on birth weight. et al (2005) for studying the economic cost of low brith weights on the society, and was further analyzed in Cattaneo (2010) and Liu et al (2016). The dataset can be found on http://www.stata-press.com/data/r13/cattaneo2.dta.…”

“…The estimation of α, η was also studied in the literature (Liu et al 2016, Ma & Zhu 2013), hence we directly write out the five step algorithm here for completeness of the content and clarity.…”

“…Robins et al (1994) proposed a class of semiparametric estimators based on inverse probability weighted (IPW) estimating equations, borrowing the idea of Horvitz & Thompson (1952) in the survey sampling literature. Later Liu et al (2016) implemented the IPW estimator with semiparametric modeling to assess the propensity score function. Following this procedure, the IPW estimator consists in constructing…”

“…Sufficient dimension reduction (Li 1991, Li & Duan 1991, Cook 1998, Xia et al 2002, Xia 2007, Ma & Zhu 2012 constitutes an alternative to covariate selection which has the advantage that it can, not only consider covariates in isolation as confounders, but also accomodate linear combinations of the whole covariate set. Such methods have only recently attracted attention in semiparametric causal inference, where Liu et al (2016) considered sufficient dimension reduction for the estimation of the propensity score only, Luo et al (2017) considered sufficient dimension reduction for the estimation of the response models only, while Ma et al (2018) considered classical sufficient dimension in all nuisance models.…”

Locally efficient semiparametric estimators for a class of Poisson models with measurement error

“…If the posited form happens to be the true conditional expectation, then the estimators will be semiparametric efficient. Such estimators are referred to as local efficient estimators, see Tsiatis & Ma (), Ma & Zhu () and Liu, Ma & Wang (). Therefore, regardless of what functional form we posit for E ( X ∣ δ ), the resulting estimator is always consistent.…”